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math.OC2026
The Exponential Price of Determinism in Nonsmooth Nonconvex Optimization
Guy Kornowski
We study the complexity of finding -Goldstein stationary points of nonsmooth nonconvex Lipschitz functions. By now, it is known that randomized first-order algorithms can so…
math.OC2026
The Complexity of Finding Stationary Points in Nonsmooth Nonconvex Optimization
Guy Kornowski
We prove that first-order algorithms require gradient queries (in the worst case) to find a -Goldstein stationary point of a Lipschitz function, at which t…
math.OC2026
Gradient Descent's Last Iterate is Often (slightly) Suboptimal
Guy Kornowski, Ohad Shamir
We consider the well-studied setting of minimizing a convex Lipschitz function using either gradient descent (GD) or its stochastic variant (SGD), and examine the last iterate conv…